Problem: Rewrite as a simplified fraction. ${2.2\overline{4} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 224.4444...\\ 10x &= 22.4444...\end{align*}}$ Subtracting the two equations, we have: ${90x = 202}$ ${x = \dfrac{202}{90}} $ ${x = \dfrac{101}{45}} \text{or} {2 \dfrac{11}{45}}$